a polymorphic transition
The same set of atoms, the same chemical composition, can lock into more than one crystal arrangement — like the same LEGO bricks that can be built into two different models. When a material switches from one of these arrangements to another as temperature or pressure changes, that switch is a polymorphic transition. For a pure element the different arrangements are called allotropes (allotropy); for a compound, polymorphs. Diamond and graphite are both pure carbon; they are polymorphs, and turning one into the other is a polymorphic transition.
Concretely: iron below 912 degrees C is BCC (alpha, ferrite); heat it past 912 degrees C and every atom rearranges into an FCC packing (gamma, austenite); past 1394 degrees C it flips back to BCC (delta). The composition never changes — only the lattice. Tin does the same, dramatically: above 13.2 degrees C it is white beta-tin (a body-centred-tetragonal metal); below, it slowly turns into grey alpha-tin (the diamond-cubic semiconductor), swelling about 27 percent and crumbling to powder — the notorious tin pest. Which polymorph is stable is set by free energy: at each temperature and pressure nature picks the structure with the lowest Gibbs free energy, and the transition happens where two structures have exactly equal free energy.
Viewed structurally (not as a heat-treatment recipe), a polymorphic transition is the atomic pattern itself reorganising, and HOW it reorganises splits into two great families — reconstructive (bonds break, atoms diffuse and re-sort) and displacive (atoms merely shift cooperatively without breaking bonds). This single idea — one composition, many structures — underlies steel (the whole art of hardening steel rides on the gamma-to-alpha iron transition), the graphite-diamond divide, the many forms of silica (quartz, tridymite, cristobalite), and pressure-driven changes deep in the Earth.
Pure iron below 912 degrees C is body-centred-cubic alpha-iron; heat it past that temperature and the whole lattice rearranges into face-centred-cubic gamma-iron — the composition never changes, only the way the atoms stack. It is precisely this reversible polymorphic transition that lets us heat steel into the gamma field and quench it, freezing in a chosen structure — the foundation of all steel heat treatment.
A polymorphic transition: atoms of one fixed composition switching between different crystal structures with temperature or pressure (as in iron's BCC to FCC).
One composition having several crystal structures is polymorphism (for an element, allotropy); do not confuse it with the different phases that appear on a phase diagram because composition changes — in a polymorphic transition the composition is fixed and only the atomic arrangement changes.